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Solutions to abstract integral equations and infinite delay evolution equations. (English) Zbl 1236.45009

The authors first establish general criteria to judge the existence of Lipschitz continuous solutions to the Cauchy problem for integral equations with infinite delay in Banach spaces. Then they give new existence theorems of strong and classical solutions to the Cauchy problem for some evolution equations with infinite delay by means of these criteria.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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Full Text: Euclid